Using half reactions, write the equation for MnO4- reacting with H2O2 in acid solution to give Mn2+ and O2

MnO4^- ==> Mn^2+

H2O2 ==> O2
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Here is a site that shows you how to do this. Follow up with any questions regarding what you don't understand.
To help you get started, Mn changes from +7 on the left to +2 on the right. O2 changes from -2 on the left (for both of them) to zero on the right (for both of them).
http://www.chemteam.info/Redox/Redox.html

To write the equation for the reaction between MnO4- and H2O2 in acid solution, it is helpful to break down the redox process into half reactions. Here's how you can do it:

Step 1: Determine the oxidation state of each element in both reactants and products.
In MnO4-, the oxidation state of Mn is +7, and in Mn2+, the oxidation state of Mn is +2. In H2O2, the oxidation state of O is -1, and in O2, the oxidation state of O is 0.

Step 2: Write the half reactions for the oxidation and reduction processes.
Oxidation half reaction: MnO4- --> Mn2+
Reduction half reaction: H2O2 --> O2

Step 3: Balance the half reactions.
First, balance the atoms other than hydrogen and oxygen in each equation. In the oxidation half reaction, we have one Mn on each side, so it is already balanced. In the reduction half reaction, we have two O on the left and one O on the right; we need to balance it by adding a coefficient of 2 in front of H2O2.

Oxidation half reaction: MnO4- --> Mn2+
Reduction half reaction: 2H2O2 --> O2

Step 4: Balance the oxygen atoms.
In the oxidation half reaction, there are four O atoms on the left and none on the right, so we need to add four H2O molecules to balance the O atoms.
Oxidation half reaction: MnO4- + 4H+ --> Mn2+ + 4H2O

Step 5: Balance the hydrogen atoms.
In the reduction half reaction, there are four H atoms on the left and four H atoms on the right, so it is already balanced. In the oxidation half reaction, we added four H+ ions to balance the O atoms, which also balances the hydrogen atoms.

Step 6: Balance the charges.
In the oxidation half reaction, we have a charge of -1 on the left and none on the right, so we need to add five electrons (e-) to balance the charges.
Oxidation half reaction: MnO4- + 4H+ + 5e- --> Mn2+ + 4H2O

In the reduction half reaction, we have a charge of 0 on the left and none on the right, so we don't need to add any electrons.

Step 7: Combine the half reactions.
To combine the half reactions, we need to make sure that the total number of electrons lost in the oxidation half reaction is equal to the total number of electrons gained in the reduction half reaction.

Multiply the oxidation half reaction by 2 and the reduction half reaction by 5 to balance the electrons:

2MnO4- + 8H+ + 10e- --> 2Mn2+ + 8H2O
5H2O2 --> 5O2

Step 8: Add both balanced half reactions together.
Add the two half reactions together to get the balanced equation for the overall reaction:

2MnO4- + 8H+ + 10H2O2 --> 2Mn2+ + 8H2O + 5O2

This is the balanced equation for the reaction between MnO4- and H2O2 in acid solution, giving Mn2+ and O2 as the products.